Preparing a metrologically-relevant entangled state includes: providing a plurality of atoms in a regular lattice, wherein each atom is in an initial quantum state of a first state in a ground state manifold; initializing a central atom in the regular lattice to a (|0+|1)/√2 state while all other atoms remain in the first state |0 as remaining atoms; and proceeding, starting with the central atom, to propagate preparation of Greenberger-Horne-Zeilinger (GHZ) states in a nonlinear progression by increasing a number of GHZ states in each iteration through the remaining atoms in a recursive manner, to produce an intermediate GHZ state, such that the intermediate GHZ state acts as an initial GHZ state for a next iteration, until a final GHZ state is formed to prepare the metrologically-relevant entangled state of the atoms.
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2. The process of claim 1, wherein the atoms comprise a neutral alkali atom, an alkaline-earth atom, an alkaline-earth-like atom, or a combination comprising at least one of the foregoing types of atoms.
3. The process of claim 1, wherein the multi-controlled and multi-target Z gate is a CkZm gate, wherein k is the number of control atoms and m is the number of target atoms.
5. The process of claim 4, wherein the drive parameters comprise Rabi frequencies and detuning frequencies of the π-polarized microwave drive and the σ-polarized microwave drive.
6. The process of claim 1, wherein the initial Rydberg states comprise an s state, a p state, or a combination comprising at least the foregoing states.
8. The process of claim 7, wherein the atoms comprise a neutral alkali atom, an alkaline-earth atom, an alkaline-earth-like atom, or a combination comprising at least one of the foregoing types of atoms.
9. The process of claim 7, wherein the multi-controlled and multi-target Z gate is a CkZm gate, wherein k is the number of control atoms and m is the number of target atoms.
11. The process of claim 10, wherein the drive parameters comprise Rabi frequencies and detuning frequencies of the π-polarized microwave drive and the σ-polarized microwave drive.
12. The process of claim 7, wherein the initial Rydberg states comprise an s state, a p state, or a combination comprising at least the foregoing states.
14. The process of claim 13, wherein the metrologically-relevant entangled state comprises the GHZ state.
15. The process of claim 13, wherein the regular lattice is a square lattice, a triangular lattice, or a honeycomb lattice.
18. The process of claim 16, wherein the metrologically-relevant entangled state comprises the GHZ state.
19. The process of claim 16, wherein the regular lattice comprises a square lattice, a triangular lattice, or a honeycomb lattice.
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November 19, 2021
July 2, 2024
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